Since I mostly build inexpensive amps, I may be of help to you.
1 - Building a kit is a very good way for a beginner to start. A good kit will have a good design that is known to work well and be safe. Along the way you will learn important lessons on how to lay out the various parts. Also worth considering is the support you will receive if you run into problems.
The Bottlehead company
http://bottlehead.com/bottlehead-products/ based near Seattle is renowned as a producer of good kit amps. They are worth checking out, both the kits and also their forum
http://www.bottlehead.com/smf/ which is a great source of support if you run into problems. I got into this hobby by building a Foreplay line stage many years ago. Unfortunately their amps are more expensive than your $250 limit but remember you are paying for a learning experience.
2 - There is a lot of advice out there for working safely with the high voltage of tube amps. This article
http://tubelab.com/safety/electrical-safety/ from the Tubelab website is very useful. I have been using his idea of using several cheap digital multimeters from Harbor Freight for many years. Even so, I still get sweaty armpits when I fire up a new amp for the first time.
3 - should not be a problem with an inexpensive amp.
4 - Building a low powered amp for less than $250 can be done. Go to this link
http://bottlenecksaudio.blogspot.com/2012/02/6v6-competition.html and scroll down to photos of a 6V6 competition held a few years back at Sterling VA a few years back where the amps had to cost less than $200 and the cases had to come from Ikea. The winning entry actually cost less than $150. Most builders had trouble staying below $200. Since you have no building experience, you are not going to be able to build any of these without help.
5 - Your power output needs will depend on the efficiency of your speakers and room size. To get an idea of power requirements, read this post by Paul Joppa
http://www.audioasylum.com/scripts/d.pl?audio/faq/sets.html. Paul is the principal designer of the Bottlehead kits.
6 - It really helps to have help on your first build. Depending on where you live, you might be able to find somebody local who might be able to help you.
Finally, the initial cost of entry into this DIY hobby might be low, but it can become much more expensive if you really get into it. But it is fun and there is nothing like listening to an amplifier that you built.
ray